
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 $a$, $b$, $c$, $d$, $e$, and $f$ be positive integers with $a+b+c+d+e+f=1800$. Let $N$ be the largest of the sum $a+b$, $b+c$, $c+d$, $d+e$, and $e+f$. What is the smallest possible value of $N$?

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