
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 $ax - y + 6 = 0$ and a circle with center $C$ defined by the equation $(x + 1)^2 + (y - a)^2 = 16$, the line intersects the circle at points $A$ and $B$. If triangle $ABC$ is a right triangle, then the positive value of $a$ equals $\_\_\_\_\_\_.$

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