
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
A box contains 13 balls, numbered from 1 through 13. If 7 balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?
A) $\frac{761}{1716}$
B) $\frac{847}{1716}$
C) $\frac{1}{2}$
D) $\frac{113}{231}$
E) $\frac{7}{13}$

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