
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 that $F_{1}$ and $F_{2}$ are the two foci of the ellipse $\frac {x^{2}}{25}+ \frac {y^{2}}{9}=1$, a line passing through $F_{1}$ intersects the ellipse at points $A$ and $B$. If $|F_{2}A|+|F_{2}B|=12$, calculate the value of $|AB|$.

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