
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 \\(f(x)=A\sin (\omega x+\phi)(A > 0,0 < \omega < 4,|\phi| < \frac {\pi}{2})\\) passes through the point \\((0, \frac {1}{2})\\), and when \\(x= \frac {\pi}{6}\\), the function \\(f(x)\\) reaches its maximum value \\(1\\).
\\((1)\\) Shift the graph of the function \\(f(x)\\) to the right by \\( \frac {\pi}{6}\\) units to obtain the function \\(g(x)\\), and find the expression for \\(g(x)\\);
\\((2)\\) Under the condition of \\((1)\\), for the function \\(h(x)=f(x)+g(x)+2\cos ^{2}x-1\\), find the range of \\(h(x)\\) on \\(\[0, \frac {\pi}{2}\]\\).

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