
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 the line $x + ay + 3 = 0$ intersects with the circle O: $x^2 + y^2 = 4$ at points A and B (with O as the origin), and $\triangle$AOB is an equilateral triangle, the value of the real number $a$ is $\_\_\_\_\_\_$.

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