
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
A bag contains 6 balls of the same size and quality, including 2 red balls and 4 green balls. Two balls are drawn without replacement.  
$(1)$ Find the probability of drawing a red ball on the second draw.  
$(2)$ Find the probability of drawing two balls of the same color.  
$(3)$ If there are 2 red balls and $n$ green balls, and the probability of drawing two red balls is $\frac{1}{21}$, what is the value of $n$?

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