
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 $A= \begin{bmatrix} 2 & 1 \\ 0 & 1 \end{bmatrix}$, and the vector $\overrightarrow{b} = \begin{bmatrix} 10 \\ 2 \end{bmatrix}$. Find the vector $\overrightarrow{a}$ such that $A^2\overrightarrow{a}=\overrightarrow{b}$.

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