
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
Given that the graphs of \( y=p(x) \) and \( y=q(x) \) intersect at \( (1,1), (3,3), (5,5), \) and \( (7,7), \) identify a point where the graphs of \( y=p(2x) \) and \( y=2q(x) \) must intersect.

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