
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
If $\mathbf{a}$ and $\mathbf{b}$ are vectors such that $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 12$, and at one instance $\mathbf{a}$ is perpendicular to $\mathbf{b}$, while at another instance they are parallel, find all possible values of $\mathbf{a} \cdot \mathbf{b}$ under these conditions.

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