
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 two vectors \(\mathbf{u}\) and \(\mathbf{z}\) such that \(\|\mathbf{u}\| = 4\), \(\|\mathbf{z}\| = 6\), and \(\mathbf{u} \cdot \mathbf{z} = 12\), find \(\|\operatorname{proj}_{\mathbf{z}} \mathbf{u}\|\).

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