
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 system of linear equations in $x$ and $y$ $$\begin{pmatrix} m & 1 \\ 1 & m\end{pmatrix}$$ $$\begin{pmatrix} x \\ y\end{pmatrix}$$ = $$\begin{pmatrix} m^{2} \\ m\end{pmatrix}$$ has infinitely many solutions, then the value of the real number $m$ is \_\_\_\_\_\_.

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