
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 vectors $\overrightarrow {a}$, $\overrightarrow {b}$, and $\overrightarrow {c}$ satisfy $\overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}= \overrightarrow {0}$, $( \overrightarrow {a}- \overrightarrow {b})\perp \overrightarrow {c}$, and $\overrightarrow {a}\perp \overrightarrow {b}$, with $| \overrightarrow {a}|=1$, 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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