
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
Read the following material before solving the problem: In mathematics, there are numbers with square roots that contain another square root, which can be simplified by using the complete square formula and the properties of quadratic surds. For example, $\sqrt{3+2\sqrt{2}}=\sqrt{3+2×1×\sqrt{2}}=\sqrt{{1^2}+2×1×\sqrt{2}+{{({\sqrt{2}})}^2}}=\sqrt{{{({1+\sqrt{2}})}^2}}=|1+\sqrt{2}|=1+\sqrt{2}$.

Solve the following problems:

$(1) \sqrt{7+4\sqrt{3}}$;

$(2) \sqrt{9-4\sqrt{5}}$.

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