
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
For non-negative integers \( x \), the function \( f(x) \) is defined as follows:
$$
f(0) = 0, \quad f(x) = f\left(\left\lfloor \frac{x}{10} \right\rfloor\right) + \left\lfloor \log_{10} \left( \frac{10}{x - 10\left\lfloor \frac{x-1}{10} \right\rfloor} \right) \right\rfloor .
$$
For \( 0 \leqslant x \leqslant 2006 \), what is the value of \( x \) that maximizes \( f(x) \)?

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