
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
$(1)$ Simplify first, then find the value: $\left(a+b\right)\left(a-b\right)+b\left(a+2b\right)-\left(a+b\right)^{2}$, where $a=-\sqrt{2}$, $b=\sqrt{6}$.<br/>$(2)$ Solve the equation: $\frac{3}{x-5}+2=\frac{x-2}{5-x}$.

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