
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
Let \( S_n \) and \( T_n \) be the sums of the first \( n \) terms of two arithmetic sequences, respectively. If for all \( n \), \(\frac{S_n}{T_n} = \frac{7n+1}{4n+27}\), find the ratio of the 11th term of the first sequence to the 11th term of the second sequence.

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