
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 circle $C$: ${(x-a)}^{2}+{(y-2)}^{2}=4$ $(a > 0)$ and line $l:x-y+3=0$, calculate the value of $a$ when the length of the chord cut by line $l$ on circle $C$ is $2 \sqrt{3}$.

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