
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
Define a function $g(x)$ for $0 \le x \le 1$ with 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) $g \left( \frac{x}{4} \right) = \frac{g(x)}{3}$ for $0 \le x \le 1.$

Determine $g \left( \frac{2}{9} \right)$.

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