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

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