
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
There are 15 chocolates lined up on a table, some of which are milk chocolates, and the rest are dark chocolates. Players A and B play the following game: Starting from the left, a player eats a continuous number of chocolates, with the requirement that the number of chocolates of the same type as the first chocolate eaten must be odd. For example, if the chocolates remaining on the table are $\operatorname{MMDMD}$ (where M represents milk chocolate and D represents dark chocolate), then a player can eat 1, 4, or 5 chocolates from the left side continuously. The player who eats the last chocolate wins. Assuming player A starts first, out of all $2^{15}$ possible different arrangements of chocolates, how many scenarios result in player B winning?

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