
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
Consider the number $15!$. The prime factorization of $15!$ results in $15! = 2^a \times 3^b \times 5^c \times 7^d \times 11^e \times 13^f$, where $a, b, c, d, e, f$ are the powers of each respective prime in the factorization of $15!$. A divisor of $15!$ is chosen at random. What is the probability that the divisor is odd?
A) $\frac{1}{8}$
B) $\frac{1}{10}$
C) $\frac{1}{12}$
D) $\frac{1}{15}$
E) $\frac{1}{20}$

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