
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
"Modulo $m$ graph paper" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \leq x < m$. To graph a congruence, we mark every point $(x, y)$ that satisfies the congruence. Consider the graphs of the following equations on modulo $9$ graph paper: $$y \equiv 2x + 3 \pmod{9}$$ and $$y \equiv 7x + 6 \pmod{9}.$$
Determine the sum of the $x$-coordinates of the points where the graphs of the two equations intersect.

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