
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
Annie takes a  $6$  question test, with each question having two parts each worth  $1$  point. On each **part**, she receives one of nine letter grades  $\{\text{A,B,C,D,E,F,G,H,I}\}$  that correspond to a unique numerical score. For each **question**, she receives the sum of her numerical scores on both parts. She knows that  $\text{A}$  corresponds to  $1$ ,  $\text{E}$  corresponds to  $0.5$ , and  $\text{I}$  corresponds to  $0$ .

When she receives her test, she realizes that she got two of each of  $\text{A}$ ,  $\text{E}$ , and  $\text{I}$ , and she is able to determine the numerical score corresponding to all  $9$  markings. If  $n$  is the number of ways she can receive letter grades, what is the exponent of  $2$  in the prime factorization of  $n$ ?

*2020 CCA Math Bonanza Individual Round #10*

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