
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 the 2022 Qatar World Cup, a total of 32 teams will compete in the final stage. The final stage is divided into group stage and knockout stage. The 32 teams are drawn into 8 groups, with 4 teams in each group, to play the group stage matches. The group stage matches are played in a round-robin format (each pair of teams in the same group plays only one match). The top two teams from each group, a total of 16 teams, will advance to the knockout stage. In the knockout stage, the 16 teams will play single-elimination matches according to a predetermined schedule without drawing lots. The matches will include the round of 16, quarter-finals, semi-finals, and the final to determine the champion and runner-up, as well as a match to determine the third and fourth place.

$(1)$ In Group $C$ of this World Cup, the 4 teams are Argentina, Saudi Arabia, Mexico, and Poland. Please create a table showing the group stage match-ups for Group $C$ (without specifying match times).

$(2)$ Please briefly explain how many matches the champion Argentina played in the final stage of this World Cup.

$(3)$ Please briefly explain how many matches the 32 teams in this World Cup played in the final stage.

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