
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" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x,y)$ where $0\le x, y <m$. The graph of $$4x\equiv 5y-1 \pmod{29}$$ has a single $x$-intercept $(x_0,0)$ and a single $y$-intercept $(0,y_0)$, where $0\le x_0, y_0<29$.

What is the value of $x_0+y_0$?

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