
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 vectors $\mathbf{a}$ and $\mathbf{b}$ be such that $\|\mathbf{a}\| = 5$, $\|\mathbf{b}\| = 8$, and the dot product $\mathbf{a} \cdot \mathbf{b} = 20$. Find the magnitude of the projection of vector $\mathbf{a}$ onto vector $\mathbf{b}$.

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