
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
The complete square formula $\left(a+b\right)^{2}=a^{2}\pm 2ab+b^{2}$ can be used to solve many mathematical problems.<br/>Please try to solve:<br/>$(1)$ If $a+b=5$ and $ab=2$, find the value of $a^{2}+b^{2}$;<br/>$(2)$ If $a+b=10$ and $a^{2}+b^{2}=50^{2}$, find the value of $ab$.

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