
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
If $\overrightarrow {a}, \overrightarrow {b}, \overrightarrow {c}$ are all unit vectors, and $\overrightarrow {a}\cdot \overrightarrow {b}=0$, $( \overrightarrow {a}+ \overrightarrow {c})\cdot ( \overrightarrow {b}+ \overrightarrow {c})\leq 0$, then the minimum value of $| \overrightarrow {a}+ \overrightarrow {b}- \overrightarrow {c}|$ is ______.

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