
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 unit vectors $\overrightarrow{e_1}, \overrightarrow{e_2}$ with $\overrightarrow{e_1} \cdot \overrightarrow{e_2} = -\frac{1}{2}$, for vector $\overrightarrow{a}$ satisfying $(\overrightarrow{a} - \overrightarrow{e_1}) \cdot (\overrightarrow{a} - \overrightarrow{e_2}) = \frac{5}{4}$, find the range of $|\overrightarrow{a}|$.

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