
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
Given the set  $X=\left\{1,2,3,4\right\}$, consider a function  $f:X\to X$ where  $f^1=f$  and  $f^{k+1}=\left(f\circ f^k\right)$  for  $k\geq1$. Determine the number of functions  $f$  that satisfy  $f^{2014}\left(x\right)=x$  for all  $x$  in  $X$.

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