
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
Determine the ratio $\frac{y}{x}$ if the matrix
\[\begin{pmatrix} \frac{1}{13} & -\frac{12}{13} \\ -\frac{12}{13} & \frac{4}{13} \end{pmatrix}\] 
corresponds to projecting onto a vector $\begin{pmatrix} x \\ y \end{pmatrix}.$

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