
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 \( 0 \leq x, y < m \). The graph of the congruence 
$$5x \equiv 3y - 2 \pmod{40}$$
has a single \( x \)-intercept \( (x_0, 0) \) and a single \( y \)-intercept \( (0, y_0) \), where \( 0 \leq x_0, y_0 < 40 \).

What is the value of \( x_0 + y_0 \)?

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