
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 vectors $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$ satisfying $\overrightarrow {a} + \overrightarrow {b} + \overrightarrow {c} = \overrightarrow {0}$, $(\overrightarrow {a} - \overrightarrow {b}) \perp \overrightarrow {c}$, $\overrightarrow {a} \perp \overrightarrow {b}$, and $|\overrightarrow {a}| = 1$, find the value of $|\overrightarrow {a}|^{2} + |\overrightarrow {b}|^{2} + |\overrightarrow {c}|^{2}$.

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