
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
Uncle Fyodor, cat Matroskin, Sharik, and postman Pechkin ate a cake (the whole cake was eaten in the end). Uncle Fyodor ate half as much as Pechkin, and cat Matroskin ate half as much as the portion of the cake that Pechkin did not eat. What fraction of the cake did postman Pechkin eat if Sharik ate only one-tenth of the cake? (Answer in decimal form.)

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