
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
Let  $x,\ y$  be real numbers. For a function  $f(t)=x\sin t+y\cos t$ , draw the domain of the points  $(x,\ y)$  for which the following inequality holds.
\[\left|\int_{-\pi}^{\pi} f(t)\cos t\ dt\right|\leq \int_{-\pi}^{\pi} \{f(t)\}^2dt.\]

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