
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
Given an ellipse $C: \frac{x^2}{m} + y^2 = 1$, there is a proposition $P$: "If $m=4$, then the eccentricity of ellipse $C$ is $\frac{\sqrt{3}}{2}$". Let $f(P)$ denote the number of true propositions among the four forms: the proposition itself, its converse, its inverse, and its contrapositive. Then $f(P) =$ ______.

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