
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

In a shooting contest, 8 targets are arranged in two columns with 3 targets and one column with 2 targets. The rules are:

- The shooter can freely choose which column to shoot at.
- He must attempt the lowest target not yet hit.

a) If the shooter ignores the second rule, in how many ways can he choose only 3 positions out of the 8 distinct targets to shoot?

b) If the rules are followed, in how many ways can the 8 targets be hit?

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