
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
Find  $\lim_{n\to\infty} \left(\frac{_{3n}C_n}{_{2n}C_n}\right)^{\frac{1}{n}}$ 

where  $_iC_j$  is a binominal coefficient which means  $\frac{i\cdot (i-1)\cdots(i-j+1)}{j\cdot (j-1)\cdots 2\cdot 1}$ .

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