
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
If  $x=\sqrt2+\sqrt3+\sqrt6$  is a root of  $x^4+ax^3+bx^2+cx+d=0$  where  $a,b,c,d$  are integers, what is the value of  $|a+b+c+d|$ ?

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