
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
Ana, Bia, Cátia, Diana, and Elaine work as street vendors selling sandwiches. Daily, they visit Mr. Manoel's snack bar and take an identical number of sandwiches to sell. One day, Mr. Manoel was sick and left a note explaining his absence and asking each vendor to take $\frac{1}{5}$ of the sandwiches. Ana arrived first, followed the note's instructions, and left to sell her sandwiches. Bia arrived next but thought she was the first and took $\frac{1}{5}$ of what was left. Cátia, Diana, and Elaine arrived together and equally divided the remaining sandwiches since Cátia knew Ana and Bia had already picked up their shares.

a) What fraction of the total sandwiches did Bia take?

b) Who received the smallest quantity of sandwiches? Who received the largest quantity?

c) By the end of the division, none of the vendors had more than 20 sandwiches. How many sandwiches did Mr. Manoel leave for them?

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