
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 deck of cards has 52 cards, with $A, J, Q, K$ considered as 1 point, 11 points, 12 points, and 13 points respectively. If we randomly draw several cards, disregarding suits, and there are definitely three cards with the same point value among them, how many cards must be drawn at least $\qquad$? If we randomly draw several cards, disregarding suits, and there are definitely two cards whose point value sums to 15 among them, how many cards must be drawn at least $\qquad$?

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