The assembly you are looking for is "Microsoft.Office.Server.Search, Version=14.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c"
See webpart definition:
<?xml version="1.0" encoding="utf-8"?>
<WebPart xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns="http://schemas.microsoft.com/WebPart/v2">
<Title>Advanced Search Box</Title>
<FrameType>None</FrameType>
<Description>Displays parameterized search options based on properties and combinations of words.</Description>
<FrameState>Normal</FrameState>
<AllowRemove>true</AllowRemove>
<AllowZoneChange>true</AllowZoneChange>
<AllowMinimize>true</AllowMinimize>
<IsVisible>true</IsVisible>
<Assembly>Microsoft.Office.Server.Search, Version=14.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c</Assembly>
<TypeName>Microsoft.Office.Server.Search.WebControls.AdvancedSearchBox</TypeName>
<TextQuerySectionLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" _locID="WP_ASB_TextSectionLabel">Find documents that have...</TextQuerySectionLabelText>
<ShowAndQueryTextBox xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowAndQueryTextBox>
<AndQueryTextBoxLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowPhraseQueryTextBox xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowPhraseQueryTextBox>
<PhraseQueryTextBoxLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowOrQueryTextBox xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowOrQueryTextBox>
<OrQueryTextBoxLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowNotQueryTextBox xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowNotQueryTextBox>
<NotQueryTextBoxLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ScopeSectionLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" _locID="WP_ASB_ScopeSectionLabel">Narrow the search...</ScopeSectionLabelText>
<ScopeLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowLanguageOptions xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowLanguageOptions>
<LanguagesLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowResultTypePicker xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowResultTypePicker>
<ResultTypeLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" />
<ShowPropertiesSection xmlns="urn:schemas-microsoft-com:AdvancedSearchBox">true</ShowPropertiesSection>
<PropertiesSectionLabelText xmlns="urn:schemas-microsoft-com:AdvancedSearchBox" _locID="WP_ASB_PropertiesSectionLabel">Add property restrictions...</PropertiesSectionLabelText>
</WebPart>