put on one's thinking cap, to

Think or reflect seriously, as in A new slogan? I'll have to put on my thinking cap for that. This term originated in the late 1800s and replaced considering cap, which dates from the early 1600s.

To take time to reflect or ponder. This term, which at first was stated as one’s considering cap, dates from the early seventeenth century. “Now I’ll put on my considering cap,” wrote John Fletcher in his play The Loyal Subject (1618). It only became a thinking cap in the late nineteenth century.