
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
If  $x, y, z, w$  are nonnegative real numbers satisfying \[\left\{ \begin{array}{l}y = x -  2003  z = 2y - 2003  w = 3z -  2003 
 \end{array} \right.
\]  find the smallest possible value of  $x$  and the values of  $y, z, w$   corresponding to it.

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