
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
A line $y=kx+1$ intersects with a circle $x^2+y^2+kx+my-4=0$ at points $P$ and $Q$. These points are symmetric with respect to the line $x+y=0$. Determine the area of the region represented by the system $\begin{cases} kx-y+1 \geqslant 0, \\ kx-my \leqslant 0, \\ y \geqslant 0. \end{cases}$

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