
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 maximum and minimum values of the function:

1) \( z = x^{2} - y^{2} + 2a^{2} \) in the circle \( x^{2} + y^{2} \leqslant a^{2} \);

2) \( v = 2x^{3} + 4x^{2} + y^{2} - 2xy \) in the closed region bounded by the lines \( y = x^{2} \) and \( y = 4 \).

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