
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
Simplify and evaluate:
$(1)e^{\ln 3}+\log_{\sqrt{5}} 25 + (0.125)^{-\frac{2}{3}}$
$(2)$ Given $\sqrt{a}+\frac{1}{\sqrt{a}}=3$, find the value of $a^2 + a^{-2}$.

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