
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 all common points of the graphs

\[
y = 8 \cos^2 (\pi x) \cdot \cos (2 \pi x) \cdot \cos (4 \pi x) \quad \text{and} \quad y = \cos (6 \pi x)
\]

with the x-coordinates belonging to the interval \([-1, 0]\). Provide the sum of the x-coordinates of the found points.

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