
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 "modulo $17$ graph paper" containing pairs of integer residues $(x,y)$ for $0\le x, y <17$. Graph the equation $$5x\equiv 3y-1 \pmod{17}.$$ What are the $x$-intercept $(x_0,0)$ and $y$-intercept $(0,y_0)$ values, and their sum $x_0+y_0$, for $0\le x_0, y_0 <17$?

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