
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 circles $C_{1}$: $x^{2}+y^{2}=4$ and $C_{2}$: $(x-a)^{2}+y^{2}=4$, where $a$ is an arbitrarily chosen real number in the interval $(0,6)$, calculate the probability that the circles intersect and have a common chord length smaller than $2\sqrt{3}$.

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