
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
Let  $n$  be an even positive integer. A sequence of  $n$  real numbers is called complete if for every integer  $m$  with  $1 \leq  m \leq  n$  either the sum of the first  $m$  terms of the sum or the sum of the last  $m$  terms is integral. Determine
the minimum number of integers in a complete sequence of  $n$  numbers.

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