
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  $a_1,a_2,a_3,a_4,a_5$  be distinct real numbers. Consider all sums of the form  $a_i + a_j$  where  $i,j \in \{1,2,3,4,5\}$  and  $i \neq j$ . Let  $m$  be the number of distinct numbers among these sums. What is the smallest possible value of  $m$ ?

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