
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
At a math contest, $75$ students are wearing blue shirts, and another $105$ students are wearing yellow shirts. The $180$ students are assigned into $90$ pairs. In exactly $30$ of these pairs, both students are wearing blue shirts. Calculate the number of pairs in which both students are wearing yellow shirts.

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