
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 $f(x)=x+ \frac {t}{x}(t > 0)$ with the following properties: the function is decreasing on $(0, \sqrt {t}]$ and increasing on $[\sqrt {t},+\infty)$.
(1) If $g(x+ \frac {1}{x})=x^{2}+ \frac {1}{x^{2}}$, find the analytical expression of $g(x)$.
(2) Given the function $h(x)= \frac {4x^{2}-12x-3}{2x+1}(x\in[0,1])$, find the range of $h(x)$ using the above properties.

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