
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
Four students, Andrey, Vanya, Dima, and Sasha, participated in a school chess tournament. Each student played two games against each of the other participants. Each win awarded 1 point, a draw awarded 0.5 points, and a loss awarded 0 points.

Given the following conditions at the end of the tournament:

- Each student scored a different number of points.
- Andrey secured first place, Dima secured second, Vanya secured third, and Sasha secured fourth.
- Andrey won the same number of games as Sasha.

How many points did each student score?

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