
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 have a sum of 34, and when two more integers are added to the first two integers, the sum is 51, and finally, when two more integers are added to the sum of the previous four integers, the sum is 72, determine the minimum number of odd integers among the 6 integers.

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