
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 $13$ graph paper", which consists of a grid of $13^2$ points with integers $(x,y)$ where $0 \leq x < 13$, we graph two congruences: $$y \equiv 3x + 4 \pmod{13}$$ and $$y \equiv 8x + 9 \pmod{13}.$$ Determine the sum of the $x$-coordinates of the points that appear on both graphs.

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