
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 $a \in \mathbb{R}$, the line $l\_1$ is defined as $(2a + 1)x + 2y - a + 2 = 0$, and the line $l\_2$ is defined as $2x - 3ay - 3a - 5 = 0$. The two lines are perpendicular.

1. Find the value of $a$.
2. Find the equation of the circle that has its center at the intersection point of $l\_1$ and $l\_2$, and is tangent to the line $3x - 4y + 9 = 0$.

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