
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
If $\overrightarrow{\alpha}, \overrightarrow{\beta}$ are a set of bases, and vector $\overrightarrow{\gamma}=x\cdot\overrightarrow{\alpha}+y\cdot\overrightarrow{\beta}$ ($x, y \in \mathbb{R}$), then $\left(x, y\right)$ is called the coordinates of vector $\overrightarrow{\gamma}$ in the bases $\overrightarrow{\alpha}, \overrightarrow{\beta}$. Given that the coordinates of vector $\overrightarrow{a}$ in the bases $\overrightarrow{p}=(1,-1), \overrightarrow{q}=(2,1)$ are $\left(-2,2\right)$, then the coordinates of $\overrightarrow{a}$ in another set of bases $\overrightarrow{m}=(-1,1), \overrightarrow{n}=(1,2)$ are ____.

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