
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
Given the function $f(x)=ax^{2}+bx$, and $1 \leqslant f(-1) \leqslant 2$, $2 \leqslant f(1) \leqslant 4$. Find the range of $f(-2)$.

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