
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 that for any real numbers \( x, y \) and \( z \), \(\oplus\) is an operation satisfying
(i) \( x \oplus 0 = 1 \), and
(ii) \( (x \oplus y) \oplus z = (z \oplus xy) + z \).
If \( 1 \oplus 2004 = c \), find the value of \( c \).

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