
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
Consider vectors $\mathbf{u}$ and $\mathbf{x}$ such that $\|\mathbf{u}\| = 5,$ $\|\mathbf{x}\| = 8,$ and $\mathbf{u} \cdot \mathbf{x} = 16$. Find the magnitude of the projection of $\mathbf{u}$ on $\mathbf{x}$ and also calculate $\|\mathbf{u} - \text{proj}_{\mathbf{x}} \mathbf{u}\|$.

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