
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
On "modulo \(9\) graph paper", two graphs are drawn from the equations:
- \(y \equiv 3x + 6 \pmod{9}\)
- \(y \equiv 7x + 3 \pmod{9}\)

What is the sum of the \(x\)-coordinates of points that both graphs have in common?

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