
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]


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(1) The focal length of the hyperbola $\dfrac{x^2}{9}-\dfrac{y^2}{m}=1$ is $10$. Find the value of the real number $m$.

(2) The coordinates of the foci of the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$ are ________.

(3) The distance from the focus to the directrix of the parabola $y^2=10x$ is ________.

(4) If two athletes, A and B, each independently choose a sports uniform of color red, white, or blue with equal probability, then the probability that they choose uniforms of the same color is ________.

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