
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
In right-angled $\triangle ABC$, all three vertices are on the unit circle $x^{2}+y^{2}=1$, and point $M\left( \frac {1}{2}, \frac {1}{2}\right)$. Calculate the maximum value of $|\overrightarrow{MA}+ \overrightarrow{MB}+ \overrightarrow{MC}|$.

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