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

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