
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
On the parade ground, 2018 soldiers are lined up in a single row. The commander can order either all soldiers standing in even positions or all soldiers standing in odd positions to leave the formation. After this order, the soldiers remaining in formation close ranks into a single row. In how many ways can the commander issue a series of 8 orders so that there are exactly 7 soldiers left in formation?

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