
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 : \mathbf {R} \to \mathbf {R} $  be a smooth function such that  $ f'(x)^2 = f(x) f''(x) $  for all  $x$ . Suppose  $f(0)=1$  and  $f^{(4)} (0) = 9$ . Find all possible values of  $f'(0)$ .

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