
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 the function \( f(x) = \frac{a}{x} - x \). If for any \( x \in \left( \frac{1}{4}, 1 \right) \), it holds that \( f(x)\left|x - \frac{1}{2}\right| \leqslant 1 \), find the range of the real number \( a \).

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