
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 $2 \vec{a}+ \vec{b}=(3,3)$ and $\vec{a}- \vec{b}=(3,0)$, find:
1. The unit vector of $\vec{b}$, denoted as $\vec{b_0}$;
2. The projection of $\vec{a}$ onto $\vec{b}$.

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