
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
Let the complex number \( z = \cos \theta + \mathrm{i} \sin \theta \) (where \( 0 < \theta < \pi \)), and \(\omega = \frac{1 - (\bar{z})^4}{1 + z^4} \). Given that \( |\omega| = \frac{\sqrt{3}}{3} \) and \(\arg \omega < \frac{\pi}{2} \), find \(\theta\).

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