
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
The set of vectors \(\mathbf{u}\) such that
\[
\operatorname{proj}_{\begin{pmatrix} 3 \\ -4 \end{pmatrix}} \mathbf{u} = \begin{pmatrix} \frac{9}{5} \\ -\frac{12}{5} \end{pmatrix}
\]
lie on a line. Enter the equation of this line in the form "y = mx + b".

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