
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 the $3 \times 3$ matrix $\mathbf{M}$ such that:
\[\mathbf{M} \mathbf{i} = c_1 \mathbf{i}, \, \mathbf{M} \mathbf{j} = c_2 \mathbf{j} + \alpha \mathbf{k}, \, \mathbf{M} \mathbf{k} = c_3 \mathbf{k},\]
where $c_1, c_2, c_3$ are constants and $\alpha$ is a non-zero constant.

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