
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
The function \( g(x) \), defined for \( 0 \leq x \leq 1 \), has the following properties:
(i) \( g(0) = 0 \)
(ii) If \( 0 \leq x < y \leq 1 \), then \( g(x) \leq g(y) \)
(iii) \( g(1-x) = 1 - g(x) \) for all \( 0 \leq x \leq 1 \)
(iv) \( g \left( \frac{x}{4} \right) = \frac{g(x)}{2} \) for \( 0 \leq x \leq 1 \)

Find \( g \left( \frac{1}{4} \right) \)

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