
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 gradient and the directional derivative in the direction of $\bar{a}=4 \bar{i}-2 \bar{j}$ for the function \(z=\ln \left(4 x^{2}+2 y^{2}\right)\) at the point \(A(-2, 4)\).

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