
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
Roll two dice consecutively. Let the number on the first die be $m$, and the number on the second die be $n$. Calculate the probability that:
(1) $m+n=7$;
(2) $m=n$;
(3) The point $P(m,n)$ is inside the circle $x^2+y^2=16$.

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