
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
Team A and Team B, each with 5 members, play a sequential knockout match in a pre-determined order. The first players of both teams compete first, and the loser is eliminated. The second player of the losing team then competes with the winner, and the loser is eliminated. This continues until all members of one team are eliminated, at which point the other team is declared the winner. Assuming each team member is equally skilled, what is the expected number of players from Team A who have not played by the time the match ends? Let $X$ represent this number. Find the mathematical expectation $E(X)$.

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