
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 $f(x)=\begin{cases} 2x+\cos x, & x\geqslant 0, \\ x(a-x), & x < 0. \end{cases}$ If the solution set of the inequality $f(x) < \pi$ with respect to $x$ is $\left( -\infty, \frac{\pi}{2} \right)$, then the range of values for the real number $a$ is ______.

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