
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 a function defined on \(\{0, 1, \cdots, 2005\}\) that takes non-negative integer values. For any variable \( x \) within its domain, the function satisfies the conditions:

\[ f(2x+1) = f(2x), \]
\[ f(3x+1) = f(3x), \]
\[ f(5x+1) = f(5x). \]

What is the maximum number of distinct values this function can take?

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