
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
fantasticbobob is proctoring a room for the SiSiEyMB with  $841$  seats arranged in  $29$  rows and  $29$  columns. The contestants sit down, take part  $1$  of the contest, go outside for a break, and come back to take part  $2$  of the contest. fantasticbobob sits among the contestants during part  $1$ , also goes outside during break, but when he returns, he finds that his seat has been taken. Furthermore, each of the  $840$  contestants now sit in a chair horizontally or vertically adjacent to their original chair. How many seats could fantasticbobob have started in?

*2019 CCA Math Bonanza Team Round #8*

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