
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 $|\overrightarrow{a}|=|\overrightarrow{b}|=1$, $|\overrightarrow{c}|=\sqrt{2}$, and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, find $\cos $〈$\overrightarrow{a}-\overrightarrow{c}$,$\overrightarrow{b}-\overrightarrow{c}$〉$.

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