
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 $m$ graph paper" for $m=17$ consists of a grid of $17^2$ points. Each point $(x,y)$ represents pairs of integer residues where $0\le x, y <17$. On this graph, we want to plot the congruence $$7x\equiv 3y + 2 \pmod{17}$$.
Find the value of $x_0 + y_0$, where $(x_0,0)$ and $(0,y_0)$ are, respectively, the $x$-intercept and $y$-intercept of the graph.

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