
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 real numbers $a_i$ ($i=1,2,3,4,5,6$) satisfy $(a_2-a_1)^2+(a_3-a_2)^2+(a_4-a_3)^2+(a_5-a_4)^2+(a_6-a_5)^2=1$. Find the maximum value of $(a_5+a_6)-(a_1+a_4)$.

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