
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
Suppose \( f(x) \) is a function defined for all real \( x \), and suppose \( f \) is invertible, meaning \( f^{-1}(x) \) exists for all \( x \) in the range of \( f \).

If the graphs of \( y = f(x^2) \) and \( y = f(x^3) \) are drawn, at how many points do they intersect?

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