
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
Given that each team earns 2 points for a win and 1 point for a loss, and to be eligible for an award, each team must earn at least 12 points in all 8 games, find the relationship that $x$ should satisfy if this team wins $x$ games in all matches.

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