
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors in space that are mutually perpendicular, and $|\overrightarrow{c}|=5$, $\overrightarrow{c}•\overrightarrow{a}=\overrightarrow{c}•\overrightarrow{b}=2\sqrt{2}$, find the minimum value of $|\overrightarrow{c}-m\overrightarrow{a}-n\overrightarrow{b}|$.

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