
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
Consider the sequence

$$
a_{n}=\cos (\underbrace{100 \ldots 0^{\circ}}_{n-1})
$$

For example, $a_{1}=\cos 1^{\circ}, a_{6}=\cos 100000^{\circ}$.

How many of the numbers $a_{1}, a_{2}, \ldots, a_{100}$ are positive?

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