
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
Given the vectors $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ in the plane, where the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $90^{\circ}$, and $|\overrightarrow{a}| = |\overrightarrow{b}| = 1$, $|\overrightarrow{c}| = 2\sqrt{3}$, and $\overrightarrow{c} = λ\overrightarrow{a} + μ\overrightarrow{b}$, calculate $λ^2 + μ^2$.

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