
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
Graphs of $$y \equiv 8x + 3 \pmod{20}$$ and $$y \equiv 14x + 15 \pmod{20}$$ on modulo $20$ graph paper intersect at some points. Determine the sum of all distinct $x$-coordinates of these points.

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