
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 a "Modulo $28$ graph paper," which consists of $28^2$ points, each representing pairs of integer residues $(x, y)$ where $0 \leq x, y < 28$. You are to graph the congruence $6x \equiv 5y - 1 \pmod{28}$. Determine the single $x$-intercept $(x_0, 0)$ and the single $y$-intercept $(0, y_0)$, ensuring $0 \leq x_0, y_0 < 28$. What is $x_0 + y_0$?

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