
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 values of real numbers  $a,\ b$  for which the function  $f(x)=a|\cos x|+b|\sin x|$  has local minimum at  $x=-\frac{\pi}{3}$  and satisfies  $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\{f(x)\}^{2}dx=2$ .

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