
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
Positive integers are arranged as follows:  
1   2   5   10   17  …  
4   3   6   11   18  …  
9   8   7   12   19  …  
16  15  14  13   20  …  
25  24  23  22   21  …  
…  
The positive integers located at the diagonal positions 1, 3, 7, 13, 21, …, form the sequence $\{a_n\}$, then $a_7=$    ; the general formula for $a_n=$    .

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