
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 vectors $\mathbf{v} = \begin{pmatrix} 1 \\ y \end{pmatrix}$ and $\mathbf{w'} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$, the projection of $\mathbf{v}$ on $\mathbf{w'}$ is found to be $\begin{pmatrix} 2 \\ -2/3 \end{pmatrix}$. Determine the value of $y$.

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