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

Find \( g \left( \frac{3}{16} \right) \).

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