
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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