
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
Solve the following questions:<br/>$(1)$ If $2^{x+3}\cdot 3^{x+3}=36^{x-2}$, what is the value of $x$?<br/>$(2)$ Given $10^{-2\alpha }=3$, $10^{-\beta }=\frac{1}{5}$, find the value of $10^{2\alpha -2\beta }$.

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