
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 polynomial  $f(x)=x^3-4\sqrt{3}x^2+13x-2\sqrt{3}$  has three real roots,  $a$ ,  $b$ , and  $c$ . Find  $$ \max\{a+b-c,a-b+c,-a+b+c\}. $$  

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