
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 sum

$$
\frac{1}{\cos \alpha \cos 2 \alpha} + \frac{1}{\cos 2 \alpha \cos 3 \alpha} + \ldots + \frac{1}{\cos (n-1) \alpha \cos n \alpha}
$$

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