
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 $a, b, c$ represent 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) $\frac{s^{2}}{4} < ab + bc + ca - \frac{2}{s} abc < \frac{7}{27} s^{2}$.

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