
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 that the angle between the unit vectors $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$ is $\theta$, and $\cos\theta = \frac{1}{4}$, if the vector $\overrightarrow{a} = \overrightarrow{e_1} + 2\overrightarrow{e_2}$, then $|\overrightarrow{a}| =$ ______.

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