
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 the function $f(x)= \dfrac{1}{{3}^{x}+ \sqrt{3}}$

$(1)$ Calculate separately $f(0)+f(1)$; $f(-1)+f(2)$;

$(2)$ Based on the results of $(1)$, infer a general conclusion and provide a proof.

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