
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
Find all triples of integer parameters \(a, b\), and \(c\) for which the system of equations

\[
\left\{\begin{array}{l}
a x + 2 y + c z = c \\
3 x + b y + 4 z = 4 b
\end{array}\right.
\]

has no solutions.

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