
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
In triangle \( \triangle ABC \), let \( a, b, c \) denote the lengths of the three sides, and let \( a+b+c=s \). Then

(1) \( \frac{13}{27} s^{2} \leqslant a^{2}+b^{2}+c^{2}+\frac{4}{s} a b c < \frac{s^{2}}{2} \);

(2) \( \frac{s^{2}}{4} < a b + b c + c a - \frac{2}{s} a b c < \frac{7}{27} s^{2} \).

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