
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 $a\in \mathbb{R}$, the function $f(x)=\left\{\begin{array}{l}\log_2(x^2-3), & x>2 \\ 3^x+a, & x\leq 2\end{array}\right.$, $f(f(\sqrt{5}))=2$, then $a=$____.

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