
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 20 graph paper," which illustrates all pairs (x,y) for integer residues where $0 \leq x < 20$, we graph the equations $$y \equiv 7x + 3 \pmod{20}$$ and $$y \equiv 13x + 17 \pmod{20}$$. Determine the sum of the x-coordinates for all points that appear in both graphs.

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