
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
The championship finals of the Chinese Volleyball Super League adopts a seven-game four-win system, which means that if one team wins four games first, that team will be the overall champion, and the competition will end. Now team A and team B are in the finals. Since the two teams have similar strengths, the probability of each team winning each game is $\frac{1}{2}$. According to past data, the ticket revenue for the first game is 5 million yuan, and the ticket revenue for each subsequent game increases by 100,000 yuan compared to the previous game. What is the probability that the total ticket revenue for the finals is exactly 45 million yuan?

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