
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
On January  $20$ ,  $2018$ , Sally notices that her  $7$  children have ages which sum to a perfect square: their ages are  $1$ ,  $3$ ,  $5$ ,  $7$ ,  $9$ ,  $11$ , and  $13$ , with  $1+3+5+7+9+11+13=49$ . Let  $N$  be the age of the youngest child the next year the sum of the  $7$  children's ages is a perfect square on January  $20$ th, and let  $P$  be that perfect square. Find  $N+P$ .

*2018 CCA Math Bonanza Lightning Round #2.3*

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