
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
How many polynomial functions $f$ of degree exactly 3 satisfy $f(x^2)=[f(x)]^2=f(f(x))$ and $f(1) = 2$?
A) 0
B) 1
C) 2
D) Finitely many but more than 2
E) Infinity

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