
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 planar vectors $\overline {a}$ and $\overline {b}$ that satisfy $| \overline {a} |=2$, $| \overline {b} |=1$, and $| \overline {a} + \overline {b} | = | \overline {a} - \overline {b} |$, find $| \overline {a} - \overline {b} |$.

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