
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
Given $\arctan a+\arctan b+\arctan c+\frac{\pi}{2}=0$, compare the sizes of the following pairs of numbers:
(1) $a b+b c+c a$ and 1;
(2) $a+b+c$ and $a b c$.

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