
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a math tournament, $68$ students wear blue shirts, and $88$ students wear yellow shirts. The $156$ students are grouped into $78$ pairs. In exactly $31$ of these pairs, both students are wearing blue shirts. Determine how many pairs have both students wearing yellow shirts.
A) 37
B) 39
C) 41
D) 44
E) 45

Present the answer in LaTex format: \boxed{Your answer}
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