
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 left and right foci of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ are $F_1$ and $F_2$, respectively. The chord $AB$ passes through point $F_1$. If the circumference of the incircle of $\triangle ABF_2$ is $\pi$, and the coordinates of points $A$ and $B$ are $(x_1,y_1)$ and $(x_2,y_2)$, respectively, then find the value of $|y_1-y_2|=$ __________.

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