
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 point M(2, 1) and the circle $x^2+y^2=4$, the equation of the tangent line passing through point M is \_\_\_\_\_\_. If the line $ax-y+4=0$ intersects the circle at points A and B, and $|AB|=2\sqrt{3}$, then $a=$ \_\_\_\_\_\_.

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