
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
For each positive integer  $n\ge 2$ , define  $k\left(n\right)$  to be the largest integer  $m$  such that  $\left(n!\right)^m$  divides  $2016!$ . What is the minimum possible value of  $n+k\left(n\right)$ ?

*Proposed by Tristan Shin*

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