
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
Consider the "Modulo $m$ graph paper" with a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<m$. Graph the congruences $$y\equiv 7x+3\pmod{20}$$ and $$y\equiv 13x+17\pmod{20}$$ on modulo $20$ graph paper. Find the sum of the $x$-coordinates of the points where these graphs intersect.

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