
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
Given the function \( f(x, y, z) \) that satisfies the following conditions for any real number \( t \):

\[ f(x+t, y+t, z+t) = t + f(x, y, z) \]
\[ f(t x, t y, t z) = t f(x, y, z) \]
\[ f(x, y, z) = f(y, x, z) = f(x, z, y) \]

Determine \( f(2000, 2001, 2002) \).

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