
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 O is the coordinate origin, the line y=x+a intersects the circle x^2+y^2=4 at points A and B. If $\overrightarrow{OA} \cdot \overrightarrow{OB}=-2$, determine the value of the real number a.

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