
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
The sum of several (not necessarily different) real numbers from  $[0,1]$  doesn't exceed  $S$ .
Find the maximum value of  $S$  such that it is always possible to partition these numbers into two groups with sums  $A\le 8$  and  $B\le 4$ .

*(I. Gorodnin)*

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