
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
Find the minimum number  $n$  such that for any coloring of the integers from  $1$  to  $n$  into two colors, one can find monochromatic  $a$ ,  $b$ ,  $c$ , and  $d$  (not necessarily distinct) such that  $a+b+c=d$ .

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