
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
Consider the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1$ with $n$ distinct points $P_1$, $P_2$, ..., $P_n$ on it. The right focus of the ellipse is $F$, and the sequence $|P_nF|$ is an arithmetic sequence with a common difference no less than $\frac{1}{100}$. Determine the maximum value of $n$.

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