
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  $F$  be an increasing real function defined for all  $x, 0 \le x \le 1$ , satisfying the conditions
(i)  $F (\frac{x}{3}) = \frac{F(x)}{2}$ .
(ii)  $F(1- x) = 1 - F(x)$ .
Determine  $F(\frac{173}{1993})$  and    $F(\frac{1}{13})$  .

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