
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 $f(x)=\begin{cases} -x^2 + x, & x \leqslant 1 \\ \log_{0.3}x, & x > 1 \end{cases}$, determine the range of the real number $t$ for which the inequality $f(x) \leqslant \frac{t^2}{4} - t + 1$ holds for any $x \in \mathbb{R}$.

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