
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
Given two integers, their sum is 30. After adding two more integers to the first two, the sum is 47. Finally, after adding two more integers to the sum of the previous four, the sum is 65. Determine the minimum number of odd integers among the six integers.

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