
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
Find the angles \(\alpha, \beta\), and \(\gamma\) of the first quadrant, given that they form an arithmetic progression with a common difference of \(\frac{\pi}{12}\), and their tangents form a geometric progression.

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