
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 two moving points A and B on the circle $x^{2}+y^{2}=5$ such that $|AB|=\sqrt{15}$, and point M moves on the line $2x+y-5=0$, calculate the minimum value of $|\overrightarrow{MA}+\overrightarrow{MB}|$.

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