
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
Given five distinct real numbers, consider all their pairwise sums. The smallest two sums are 20 and 200, while the largest two sums are 2014 and 2000. Determine the range of the smallest number, \( a \), among these five real numbers.

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