
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  $f(n)=\frac{n}{3}$  if  $n$  is divisible by  $3$  and  $f(n)=4n-10$  otherwise.  Find the sum of all positive integers  $c$  such that  $f^5(c)=2$ . (Here  $f^5(x)$  means  $f(f(f(f(f(x)))))$ .)

*Proposed by Justin Stevens*

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