
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) $g\left(\frac{x}{4}\right) = \frac{g(x)}{3}$ for $0 \leq x \leq 1.$

Find $g\left(\frac{3}{5}\right).$

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