
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 lengths of the 3 sides of $\triangle LMN$ are 8, 15, and 17 respectively. If the area of $\triangle LMN$ is $A$, find $A$.

If $r$ is the length of the radius of the circle inscribed in $\triangle LMN$, find $r$.

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