
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
The numbers  $1,2,\dots,10$  are written on a board. Every minute, one can select three numbers  $a$ ,  $b$ ,  $c$  on the board, erase them, and write  $\sqrt{a^2+b^2+c^2}$  in their place. This process continues until no more numbers can be erased. What is the largest possible number that can remain on the board at this point?

*Proposed by Evan Chen*

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