
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
Find the derivatives of the following functions:
1) $y = x^{3} \cdot 3^{x}$.
2) $f(x) = \sqrt[x]{3} + \frac{1}{25^{5x}} + 6^{1/x}$; calculate $f^{\prime}(1)$.
3) $y = \ln (\cos(3x))$.
4) $r = a^{4} b^{\prime \prime} c^{\prime \prime} + \log_{10}(5p) - 4 \log_{10}(\sqrt{\varphi})$.
5) $y = \ln \left( \frac{a^{2} - x^{2}}{a^{2} + x^{2}} \right)$.
6) $y = \ln \sqrt{\frac{e^{3x}}{1+e^{3x}}}$; calculate $y^{\prime}(0)$.

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