
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 the matrix equation $\begin{pmatrix} a & 2 \\ 2 & a\end{pmatrix} \begin{pmatrix} x \\ y\end{pmatrix} = \begin{pmatrix} a+2 \\ 2a\end{pmatrix}$ represents a system of linear equations in $x$ and $y$ that has no solution, then the real number $a=$ \_\_\_\_\_\_.

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