
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 hyperbola $C: x^{2}- \frac {y^{2}}{24}=1$ with its left and right foci $F_{1}$, $F_{2}$ respectively, let $P$ be a point on the first quadrant of the hyperbola $C$. If $\frac {|PF_{1}|}{|PF_{2}|}= \frac {5}{4}$, find the area of the incircle of $\triangle PF_{1}F_{2}$.

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