
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
Let's find the projection of the vector \(\begin{pmatrix} 2 \\ 0 \\ 3 \end{pmatrix}\) onto the vector \(\mathbf{u}\) if the projection of \(\begin{pmatrix} 1 \\ 2 \\ 6 \end{pmatrix}\) onto \(\mathbf{u}\) results in \(\begin{pmatrix} -1 \\ -2 \\ -6 \end{pmatrix}\).

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