
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
At least  $ n - 1$  numbers are removed from the set  $\{1, 2, \ldots, 2n - 1\}$  according to the following rules:
(i) If  $ a$  is removed, so is  $ 2a$ ;
(ii) If  $ a$  and  $ b$  are removed, so is  $ a \plus{} b$ .
Find the way of removing numbers such that the sum of the remaining numbers is maximum possible.

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