
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 \[g(x) = \left\{
\begin{array}{cl}
\frac{x}{28} & \text{ if }x\text{ is a multiple of 4 and 7}, \\
4x & \text{ if }x\text{ is only a multiple of 7}, \\
7x & \text{ if }x\text{ is only a multiple of 4}, \\
x+4 & \text{ if }x\text{ is not a multiple of 4 or 7}.
\end{array}
\right.\]If $g^a(x)$ denotes the function nested $a$ times, find the smallest value of $a$ greater than 1 such that $g(2)=g^a(2)$.

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