
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
Amandine and Brennon play a turn-based game, with Amadine starting.
On their turn, a player must select a positive integer which cannot be represented as a sum of multiples of any of the previously selected numbers.
For example, if  $3, 5$  have been selected so far, only  $1, 2, 4, 7$  are available to be picked;
if only  $3$  has been selected so far, all numbers not divisible by three are eligible.
A player loses immediately if they select the integer  $1$ .

Call a number  $n$  *feminist* if  $\gcd(n, 6) = 1$  and if Amandine wins if she starts with  $n$ . Compute the sum of the *feminist* numbers less than  $40$ .

*Proposed by Ashwin Sah*

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