
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
Sir Alex is coaching a soccer team of  $n$  players of distinct heights. He wants to line them up so that for each player  $P$ , the total number of players that are either to the left of  $P$  and taller than  $P$  or to the right of  $P$  and shorter than  $P$  is even. In terms of  $n$ , how many possible orders are there?

*Michael Ren*

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