
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 $f(x) = \ln x - x^2 + x$,  
find the interval where the function $f(x)$ is monotonically decreasing:  
(2) If for any $x > 0$, the inequality $f(x) \leqslant \left(\frac{a}{2} - 1\right)x^2 + ax - 1$ always holds, find the minimum value of the integer $a$.

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