
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 that the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is 90°, and $|\overrightarrow{a}|=|\overrightarrow{b}|=1$, $|\overrightarrow{c}|=2\sqrt{3}$, find the value of $\lambda^2+\mu^2$ where $\overrightarrow{c}=\lambda\overrightarrow{a}+\mu\overrightarrow{b}$.

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