
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) Convert the binary number $110011_{(2)}$ to a decimal number.

(2) For any real number $x$, if the inequality $(a-2)x^{2}-2(a-2)x-4 < 0$ always holds, then the set of values for the real number $a$ is ______.

(3) The minimum value of the function $y=\log_{2}(x+ \frac{1}{x-1}+5)$ $(x > 1)$ is ______.

(4) Given a geometric sequence $\{a_{n}\}$ that satisfies $a_{1}+a_{3}=10$ and $a_{2}+a_{4}=5$, the maximum value of $a_{1} \cdot a_{2} \cdots a_{n}$ is ______.

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