
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
In a similar game, Barbara and Jenna play with a turn-based rule to remove coins from a table. This time, Barbara can remove either $3$ or $5$ coins on her turn, while Jenna can remove either $2$ or $4$ coins. The game starts with Barbara's turn unless a random coin flip decides otherwise. Whoever takes the last coin wins. Given that both players use their best strategic moves, decide who will win when the game starts with $2023$ coins.
A) Barbara will win with 2023 coins.
B) Jenna will win with 2023 coins.
C) Whoever goes first will win with 2023 coins.
D) Whoever goes second will win with 2023 coins.

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