
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 $a$, $b$, $c$ be the lengths of the sides of a right-angled triangle, with $h$ being the height to the hypotenuse, and $c$ being the length of the hypotenuse. Four propositions are given:

$(1) a+b > c+h$; $(2) a^{2}+b^{2} < c^{2}+h^{2}$; $(3) a^{3}+b^{3} > c^{3}+h^{3}$; $(4) a^{4}+b^{4} < c^{4}+h^{4}$.

Among these, the true propositions are _______, and the general conclusion that can be drawn by analogy is _______.

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