
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
$F_{1}$, $F_{2}$ are the two foci of the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{45}=1$, $P$ is a point on the hyperbola. It is known that $|PF_{1}|$, $|PF_{2}|$, $|F_{1}F_{2}|$ form an arithmetic sequence in order, and the common difference is greater than $0$. Then, $\angle F_{1}PF_{2}=$ ______.

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