
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 $\frac {x^{2}}{8} + \frac {y^{2}}{6} = 1$ with n distinct points $P_{1}, P_{2}, \dots, P_{n}$ on it, and the right focus denoted as F. The sequence $\{|P_{n}F|\}$ forms an arithmetic sequence with a common difference greater than $\frac {1}{5}$. Determine the maximum value of n.

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