
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 certain basketball shooting game, the rules are as follows: each round consists of up to three shots, stopping once the first shot is made. Scoring is as follows: making the first shot scores 8 points; missing the first shot but making the second scores 6 points; missing the first two shots but making the third scores 4 points; missing all three shots scores 0 points. If a player has a 0.5 probability of making each shot, then the expected score $X$ per round of the game is.

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