
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 $f(x)= \begin{cases} \log_{2}(x+1), & x > 0 \\ -x^{2}+2x, & x\leqslant 0 \end{cases}$, find the range of values for $a$ such that $|f(x)|\geqslant ax$.

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