
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
A function  $f$  defined on integers such that $f (n) =n + 3$  if  $n$  is odd $f (n) = \frac{n}{2}$  if  $n$  is even

If  $k$  is an odd integer, determine the values for which  $f (f (f (k))) = k$ .

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