
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
A matrix \[\mathbf{R} = \begin{pmatrix} p & q \\ -\frac{4}{7} & -\frac{3}{7} \end{pmatrix}\] is such that $\mathbf{R}^2 = -\mathbf{I}$. Find the ordered pair $(p, q).$

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