
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 $P$ be any point on the right branch of the hyperbola $C: \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$, given $A(a, b)$ and $B(a, -b)$. If $\overrightarrow{OP} = λ\overrightarrow{OA} + μ\overrightarrow{OB}$ ($O$ is the origin of the coordinate system), then calculate the minimum value of $λ^{2} + μ^{2}$.

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