
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
Let  $n$  and  $k$  be integers satisfying  $\binom{2k}{2} + n = 60$ .  It is known that  $n$  days before Evan's 16th birthday, something happened.  Compute  $60-n$ .

*Proposed by Evan Chen*

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