
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
Who is richer? (For 9th grade. 4 points). The cat Basilio and the fox Alice have no more money left. Therefore, they are hired to set up and take down decorations at Karabas Barabas's theater. Every evening after the performance, Karabas gives them a coin of one soldo, and a fight immediately starts between the cat and the fox.

With a probability of 0.25, the cat wins and takes the coin for himself, with a probability of 0.25, the fox wins and takes the coin for herself, and with a probability of 0.5, both are taken to the police and all their money is confiscated (not only today's but all the money they have). Question: by how many soldos will one of the companions have more than the other at the end of the 10th day of work (the absolute difference in their wealth)? Find the expected value of this amount.

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