
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 $a \neq 0$, for the function $f(x) = \begin{cases} 4\log_{2}(-x), & \text{if } x < 0 \\ |x^2 + ax|, & \text{if } x \geq 0 \end{cases}$. If $f[f(-\sqrt{2})]=4$, find the value of $f(a)$.

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