
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
Nine weights are placed in a scale with the respective values  $1kg,2kg,...,9kg$ . In how many ways can we place six weights in the left side and three weights in the right side such that the right side is heavier than the left one?

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