
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
Jane is working on a graphics design project where she needs to find the projection of a vector $\begin{pmatrix} 3 \\ 3 \end{pmatrix}$ onto another vector. During the processing, one specific projection was calculated which took vector $\begin{pmatrix} 6 \\ -2 \end{pmatrix}$ to $\begin{pmatrix} \frac{30}{5} \\ \frac{-10}{5} \end{pmatrix}.$ What will be the projection of vector $\begin{pmatrix} 3 \\ 3 \end{pmatrix}$ onto the same vector it is being projected?

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