
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
For $\mathbf{v} = \begin{pmatrix} 2 \\ y \end{pmatrix}$ and $\mathbf{w} = \begin{pmatrix} 7 \\ 2 \end{pmatrix}$,
\[\text{proj}_{\mathbf{w}} \mathbf{v} = \begin{pmatrix} 8 \\ \frac{16}{7} \end{pmatrix}.\]Find $y$.

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