
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
Establish necessary and sufficient conditions on the constant  $k$  for the existence of a continuous real valued function  $f(x)$  satisfying   $$ f(f(x))=kx^9 $$   for all real  $x$ .

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