
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
What is the correct ordering of the three numbers $\frac{4}{13}$, $\frac{15}{31}$, and $\frac{12}{37}$, in order of increasing value?
A) $\frac{4}{13} < \frac{12}{37} < \frac{15}{31}$\
B) $\frac{12}{37} < \frac{15}{31} < \frac{4}{13}$\
C) $\frac{15}{31} < \frac{4}{13} < $\frac{12}{37}$\
D) $\frac{12}{37} < $\frac{4}{13} < \frac{15}{31}$\
E) $\frac{15}{31} < \frac{12}{37} < \frac{4}{13}$

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