
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
When the vectors \( \begin{pmatrix} -3 \\ 4 \end{pmatrix} \) and \( \begin{pmatrix} 1 \\ 6 \end{pmatrix} \) are both projected onto the same vector \( \mathbf{v}, \) the result is \( \mathbf{p} \) in both cases. Find \( \mathbf{p}. \)

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