
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 the line $x+y-a=0$ intersects the circle $x^2+y^2=2$ at points A and B, with point O being the origin, and the vectors $\overrightarrow{OA}$, $\overrightarrow{OB}$ satisfy the condition $|2\overrightarrow{OA}-3\overrightarrow{OB}|=|2\overrightarrow{OA}+3\overrightarrow{OB}|$, find the value of the real number $a$.

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