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(CNN Buiness) —  

The Dow and Nasdaq hit new records for a second straight day on Tuesday, as hopes over a pause for the trade war boosted investor sentiment.

Since the United States and China agreed to a “phase one” trade deal in October, the progress seemed to have stalled as it remains unclear when and where the two parties will sign the agreement.

Still, there is good news: the United States is assessing current tariffs on Chinese imports as the parties work to finalize the “phase one” trade deal, according to officials. No decisions have been made beyond the previously announced tariff relief.

Stocks “look to extend the market’s rally amid growing optimism that, as part of phase one of trade talks, the US will suspend tariffs on $156 billion of Chinese imports scheduled to take effect on December 15 and possibly roll back the September 1 tariffs on about $110 billion in goods,” wrote Sal Guatieri, senior economist at BMO, in a note to clients.

The Dow (INDU) finished the day up 0.2%, or some 30 points while the Nasdaq Composite (COMP) inched up 1.48 points. Both benchmarks closed at a fresh all-time high. The S&P 500 (SPX) was down about 0.1%. All three indexes hit all-time highs on Monday.

Economic data also continues to help the bullish backdrop. The Institute of Supply Management’s nonmanufacturing index climbed to 54.7 in October, beating estimates of 53.5.

Any reading above 50 denotes economic growth in the sector. In September, the index dropped sharply below expectations, fueling fears over contagion from the downturn in manufacturing.