
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 that the coefficient of $x^2$ in the expansion of $(1+ax)(1+x)^5$ is 5, find the value of $a$.
(2) Given that $a > 0$, the function $f(x)=\ln x+\frac{1}{ax}$ is an increasing function on $[1,+\infty)$. Find the range of values of $a$.
(3) Given that the complex number $z$ satisfies $z(1+i)=1$ (where $i$ is the imaginary unit), find the conjugate of $z$, denoted as $\bar{z}$.
(4) Compute $-i+\frac{1}{i}$.

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