
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
Determine the coefficients $a, b, c$ given that the following system of equations has no solution, but if $|x-1|$ is written instead of $x-1$ in the second equation, the pair $x = \frac{3}{4}, y = \frac{5}{8}$ satisfies the new system of equations.

\[
\begin{aligned}
& a(x-1) + 2y = 1 \\
& b(x-1) + cy = 3
\end{aligned}
\]

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