
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 50 cards laid out in a row on the table, numbered from 1 to 50 from left to right. Each card is blue on the bottom and red on the top. Vasya randomly selects 25 consecutive cards and flips them. Then Asya approaches the table and does the same thing - selects a random sequence of 25 consecutive cards and flips them, independent of Vasya's actions. Which card (or cards) has the lowest probability of being red-side up after all flips?

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