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WASHINGTON – In a test of divided government, President Barack Obama and House Speaker John Boehner sought an elusive compromise Tuesday to prevent economy-damaging tax increases on the middle class at year’s end, conferring by phone after a secretive exchange of proposals.

Details were sparse and evidence of significant progress scarcer still, although officials said the president had offered to reduce his initial demand for $1.6 trillion in higher tax revenue over a decade to $1.4 trillion.