
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 vectors $\overrightarrow {a} = (1, -3, 2)$, $\overrightarrow {b} = (-2, 1, 1)$, and points A$(-3, -1, 4)$, B$(-2, -2, 2)$:
1. Find the magnitude $|2\overrightarrow {a} + \overrightarrow {b}|$;
2. Determine if there exists a point E on line AB such that $\overrightarrow {OE}$ is perpendicular to $\overrightarrow {b}$ (with O being the origin).

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