
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
There are 2002 cards on the table with numbers \(1, 2, 3, \ldots, 2002\). Two players take turns picking one card at a time. After all the cards have been taken, the winner is the one whose last digit of the sum of the numbers on their taken cards is greater. Which player can always win regardless of how the opponent plays, and how should they play to achieve this?

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