
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
Some integers, when divided by $\frac{5}{7}, \frac{7}{9}, \frac{9}{11}, \frac{11}{13}$ respectively, yield mixed numbers where the fractional parts are $\frac{2}{5}, \frac{2}{7}, \frac{2}{9}, \frac{2}{11}$ respectively. What is the smallest integer greater than 1 that satisfies these conditions?

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