
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
$\sqrt{3 x} \cdot \sqrt{2 x^{2}}$

$\sqrt{3} \cdot x \cdot \sqrt{2} \cdot x^{2}$

$\sqrt{\sqrt{3 x^{2}}+\sqrt{2 x}} \cdot \sqrt{\sqrt{5 x^{2}}+\sqrt{4 x}}$

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