
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
$(1)$ Given two congruent triangles, where the lengths of one triangle's sides are $6$, $8$, $10$, and the lengths of the other triangle's sides are $6$, $2m-2$, $n+1$. Find the values of $m$ and $n$;<br/>$(2)$ Given an isosceles triangle with a perimeter of $16$, where one side is $5$, find the lengths of the legs and the base.

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