
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
Given the fractional equation about $x$: $\frac{x+a}{x-2}-\frac{5}{x}=1$.<br/>$(1)$ If the solution of the fractional equation is $x=5$, find the value of $a$;<br/>$(2)$ If $a=5$, find the solution of the fractional equation.

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