
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 the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$, a line $L$ passing through the right focus $F$ of the ellipse intersects the ellipse at points $A$ and $B$, and intersects the $y$-axis at point $P$. Suppose $\overrightarrow{PA} = λ_{1} \overrightarrow{AF}$ and $\overrightarrow{PB} = λ_{2} \overrightarrow{BF}$, then find the value of $λ_{1} + λ_{2}$.

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