
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 2022 Qatar World Cup is the 22nd FIFA World Cup, the first to be held in Qatar and the Middle East. A beloved football team always conducts data analysis on player usage. According to past statistics, player $A$ can play as a center forward, winger, and attacking midfielder, with appearance rates of $0.2$, $0.5$, and $0.3$ respectively. The probabilities of the team losing when player $A$ plays as a center forward, winger, and attacking midfielder are $0.4$, $0.2$, and $0.2$ respectively. When player $A$ participates in a match, the probability of the team not losing a game is ____.

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