
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 between 0 and $2\pi$, other than integer multiples of $\frac{\pi}{2}$, such that $\sin \theta$, $\cos \theta$, and $\tan \theta$ form a geometric sequence in some order where the common ratio is not equal to 1 or -1.

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