
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
In what case does the system
$$
\begin{array}{l}
x+y+m z=a, \\
x+m y+z=b, \\
m x+y+z=c,
\end{array}
$$
have a solution? Find the conditions under which the unique solution of the above system is an arithmetic progression.

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