
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
Two vectors, \( \begin{pmatrix} -7 \\ 2 \end{pmatrix} \) and \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} \), are projected onto the same vector \( \mathbf{v} \), resulting in the same projection \( \mathbf{p} \) for both. Find \( \mathbf{p} \).

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