
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 $\frac{x^2}{25} + \frac{y^2}{16} = 1$. The left and right foci are respectively F<sub>1</sub> and F<sub>2</sub>.
(1) Find the distance from the right focus F<sub>2</sub> to the corresponding directrix;
(2) If the distance from a point P in the first quadrant on the ellipse to the right directrix is $\frac{16}{3}$, find the distance from point P to the left focus F<sub>1</sub>.

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