
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 the sequences {a_n} and {b_n} are arithmetic sequences with the sums of their first n terms being S_n and T_n, respectively, and that S_n / T_n = (2n) / (3n + 1), determine the limit as n approaches infinity of (a_n) / (b_n).

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