
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 two vectors in the plane, $\overrightarrow{\alpha}$ and $\overrightarrow{\beta}$, with $|\overrightarrow{\alpha}|=1$ and $|\overrightarrow{\beta}|=2$, and $\overrightarrow{\alpha}$ is perpendicular to $(\overrightarrow{\alpha} - 2\overrightarrow{\beta})$, find the value of $|2\overrightarrow{\alpha} + \overrightarrow{\beta}|$.

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