
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
Dasha wrote the numbers $9,10,11, \ldots, 22$ on the board and then erased one or more of them. It turned out that the remaining numbers on the board cannot be divided into groups such that the sums of the numbers in each group are equal. What is the maximum possible sum of the remaining numbers on the board?

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