
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 $$2 \overrightarrow {a}+ \overrightarrow {b}=(3, 3), \overrightarrow {a}- \overrightarrow {b}=(3, 0)$$.
Find (1) the unit vector $$\overrightarrow {b_{0}}$$ of $$\overrightarrow {b}$$;
(2) the projection of $$\overrightarrow {a}$$ in the direction of $$\overrightarrow {b}$$.

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