
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
We will call a natural number \( n \) squareable if the numbers from 1 to \( n \) can be arranged in such a way that each member of the sequence, when added to its position number, results in a perfect square. For example, the number 5 is squareable because the numbers can be arranged like this: 32154, where \(3+1=4\), \(2+2=4\), \(1+3=4\), \(5+4=9\).

Determine which of the following numbers are squareable: 7, 9, 11, 15.

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