
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
When the expression \(\left[(1+x)\left(1+2 x^{3}\right)\left(1+4 x^{9}\right)\left(1+8 x^{27}\right)\left(1+16 x^{81}\right)\left(1+32 x^{243}\right)\left(1+64 x^{729}\right)\right]^{2}\) is expanded and simplified, find the coefficient of \(x^{2003}\).

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