
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]


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Given a permutation \((b_1, b_2, b_3, b_4, b_5, b_6)\) of \((1,2,3,4,5,6)\), determine the number of permutations satisfying the conditions that the sum of the first three elements is less than the sum of the last three elements and \(b_3\) is even.

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