
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
In a plane Cartesian coordinate system, let $e$ be a unit vector. Vector $\boldsymbol{a}$ satisfies $\boldsymbol{a} \cdot \boldsymbol{e} = 2$, and the inequality $|\boldsymbol{a}|^{2} \leqslant 5|\boldsymbol{a} + t \boldsymbol{e}|$ holds for any real number $t$. Determine the range of $|\boldsymbol{a}|$.

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