
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 $\mathbf{a}$ and $\mathbf{b}$ be vectors with magnitudes $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 8$. There is a third vector $\mathbf{c}$ such that $\|\mathbf{c}\| = 3$ and $\mathbf{c}$ is orthogonal to $\mathbf{b}$. Find all possible values of $\mathbf{a} \cdot (\mathbf{b} + \mathbf{c})$.

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