
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 $\mathbf{p},$ $\mathbf{q},$ $\mathbf{r},$ $\mathbf{s}$ be four distinct unit vectors in space such that
\[\mathbf{p} \cdot \mathbf{q} = \mathbf{p} \cdot \mathbf{r} = \mathbf{q} \cdot \mathbf{r} = \mathbf{q} \cdot \mathbf{s} = \mathbf{r} \cdot \mathbf{s} = -\frac{1}{7}.\] Find $\mathbf{p} \cdot \mathbf{s}.$

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