
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 a circle C: $x^2+y^2+4x-4ay+4a^2+1=0$ and a line $l: ax+y+2a=0$.
1. When $a= \frac{3}{2}$, the line $l$ intersects circle $C$ at points $A$ and $B$. Find the length of chord $AB$.
2. If $a>0$ and the line $l$ is tangent to circle $C$, find the equation of the circle $C'$ that is symmetrical to circle $C$ with respect to line $l$.

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