
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
Given \( a \neq 0 \), solve for \( x \) in
\[
\begin{vmatrix} 2x + a & x  & x \\ x & x + a & x \\ x & x & x + a \end{vmatrix} = 0.
\]
Provide your answer in terms of \( a \).

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