
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
A "math magician" performs tricks using green, yellow, blue, and red cards, numbered 1 to 13 for each color. He mixes the cards and tells a child: "Without me seeing, choose a card, double the number on the card, add 3, and then multiply the result by 5. Then

add 1 if the card is green;

add 2 if the card is yellow;

add 3 if the card is blue;

add 4 if the card is red.

Tell me the final result, and I will tell you the color and number of the card you chose."

a) Joãozinho chose the red card with the number 3. What number should he say to the magician?

b) Mariazinha said "seventy-six" to the magician. What is the number and color of the card she chose?

c) After choosing a card, Pedrinho said "sixty-one" and the magician replied, "You made a calculation error." Explain how the magician knew this.

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