
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
In a deck of 13 playing cards where $J, Q, K$ are valued at $11, 12, 13$ points respectively, what is the maximum number of cards that can be selected such that there are no two pairs of cards whose sums of points are equal?

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