
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

$$
y=8 \cos \pi x \cdot \cos ^{2} 2 \pi x \cdot \cos 4 \pi x \quad \text{and} \quad y=\cos 9 \pi x
$$

with abscissae belonging to the segment \( x \in [0, 1] \). In the answer, indicate the sum of the abscissae of the found points.

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