
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
The two foci of the ellipse $\dfrac{x^{2}}{25}+ \dfrac{y^{2}}{4}=1$ are $F_1$ and $F_2$. A line passing through $F_2$ intersects the ellipse at points $A$ and $B$. If $|AB|=8$, find the value of $|AF_1| + |BF_1|$.

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