
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
Calculate using the knowledge you have learned:<br/>
$(1)$ Given $a \gt b$, and $a^{2}+b^{2}=13$, $ab=6$, find the value of $a-b$;<br/>
$(2)$ Given $a$, $b$, and $c$ are the three sides of right triangle $ABC$, if $a^{2}+b^{2}+25=6a+8b$, find the perimeter of right triangle $ABC$.

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