
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 \( m \) be an integer greater than 1, and let's define a sequence \( \{a_{n}\} \) as follows:
\[
\begin{array}{l}
a_{0}=m, \\
a_{1}=\varphi(m), \\
a_{2}=\varphi^{(2)}(m)=\varphi(\varphi(m)), \\
\vdots \\
a_{n}=\varphi^{(n)}(m)=\varphi\left(\varphi^{(n-1)}(m)\right),
\end{array}
\]
where \( \varphi(m) \) is the Euler's totient function.

If for any non-negative integer \( k \), \( a_{k+1} \) always divides \( a_{k} \), find the greatest positive integer \( m \) not exceeding 2016.

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