
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
(1) Given the functions $f(x)$ and $g(x)$, it is known that $f(6)=5$, $g(6)=4$, $f'(6)=3$, and $g'(6)=1$. If $h(x)=f(x) \cdot g(x)-1$, find the value of $h'(6)$;
(2) Can the line $y= \frac {1}{2}x+b$ serve as a tangent line to the graph of the function $f(x)=\sin x$? If so, find the coordinates of the point of tangency; if not, briefly explain why.

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