
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 $17$ graph paper" consists of a grid of $17^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x<17$. Given the graphs of $$y\equiv 7x+3\pmod{17}$$ and $$y\equiv 13x+14\pmod{17}$$ on modulo $17$ graph paper, find the sum of the $x$-coordinates of the points they have in common.

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