
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 \[f(x) = \left\{
\begin{array}{cl}
\frac{x}{14} & \text{ if }x\text{ is a multiple of 2 and 7}, \\
2x & \text{ if }x\text{ is only a multiple of 7}, \\
7x & \text{ if }x\text{ is only a multiple of 2}, \\
x+2 & \text{ if }x\text{ is not a multiple of 2 or 7}.
\end{array}
\right.\]If $f^a(x)$ means the function is nested $a$ times, what is the smallest value of $a$ greater than 1 that satisfies $f(3)=f^a(3)$?

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