
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 the function \( f(x) = \left| 2 - \log_3{x} \right| \). Given that the positive real numbers \( a, b, c \) satisfy \( a < b < c \) and \( f(a) = 2 f(b) = 2 f(c) \), find the value of \( \frac{a c}{b} \).

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