
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 $|$$\overrightarrow {a}$$ $|=2$, $|$$\overrightarrow {b}$$ $|=1$, and ($$\overrightarrow {a}$$ $-2$$\overrightarrow {b}$$) • (2$$\overrightarrow {a}$$ + $$\overrightarrow {b}$$) = 9, find $|$$\overrightarrow {a}$$ + $\overrightarrow {b}$$ $|.

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