
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
Let the letters \(a, b, c, x, y, z\) represent segments, and the letters \(\alpha, \beta, \gamma\) represent angles. What types of geometric quantities are depicted by the expressions: 
1) \(a^{2} + bc\); 
2) \(\frac{ab^{2}}{xy}\); 
3) \(\frac{(a+b)^{3} + c^{3}}{x}\); 
4) \(ab \sqrt{xy}\);
5) \(\sqrt{a^{2} + b^{2} + c^{2}} \cdot (\sin \alpha + \sin \beta + \sin \gamma)\); 
6) \(\frac{a^{3} + bcx}{y} \operatorname{tg}\alpha \cdot \operatorname{tg}\beta \cdot \operatorname{tg}\gamma\).

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