
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 17 graph paper," denote the intercepts of the graph of the equation $$5x \equiv 3y + 2 \pmod{17}.$$ Determine the sum of the $x$-intercept and $y$-intercept (where both intercepts $(x_0, 0)$ and $(0, y_0)$ exist and are unique within the range $0 \leq x_0, y_0 < 17$).

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