
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
Determine the number of angles \(\theta\) between 0 and \(2\pi\), other than integer multiples of \(\pi / 2\), such that the quantities \(\sin \theta\), \(\cos \theta\), and \(\tan \theta\) form a geometric sequence in some order.

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