
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

Calculate the areas of shapes bounded by the lines given in polar coordinates.

$$
r=\cos \phi, r=\sqrt{2} \sin \left(\phi-\frac{\pi}{4}\right),\left(-\frac{\pi}{4} \leq \phi \leq \frac{\pi}{2}\right)
$$

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