
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 function $f(x)$ defined on $(0, \frac{\pi}{2})$, where $f''(x)$ is its derivative and $f''(x) \cdot \sin x - \cos x \cdot f(x) > 0$ always holds true. Determine the relationship between $\sqrt{3}f(\frac{\pi}{4})$ and $\sqrt{2}f(\frac{\pi}{3})$.

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