
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 \( 0 < a < \sqrt{3} \sin \theta \) where \( \theta \in \left[ \frac{\pi}{4}, \frac{5\pi}{6} \right] \), find the minimum value of \( f(a, \theta) = \sin^{3} \theta + \frac{4}{3a \sin^{2} \theta - a^{3}} \).

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