
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
How many integer roots of the equation

$$
\cos 2 \pi x + \cos \pi x = \sin 3 \pi x + \sin \pi x
$$

lie between the roots of the equation \( x^2 + 10x - 17 = 0 \)?

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