
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 function $f(x)=\left\{{\begin{array}{l}{{x^2}+1,-1≤x＜1}\\{2x+3,x＜-1}\end{array}}\right.$.<br/>$(1)$ Find the value of $f\left(f\left(-2\right)\right)$;<br/>$(2)$ If $f\left(a\right)=2$, find the value of $a$.

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