
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
Given the function $f(x)=\ln x-x^{2}+x$.
(1) Find the interval where the function $f(x)$ is monotonically decreasing.
(2) If the graph of the function $h(x)=(a-1)x^{2}+2ax-1$ is entirely above the graph of the function $f(x)$ on the right side of the $y$-axis, find the minimum value of the integer $a$.

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