
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
Simplify the following expression: $(2x^{10} + 8x^9 + 3x^8) + (5x^{12} - x^{10} + 2x^9 - 5x^8 + 4x^5 + 6).$ Express your answer as a polynomial with the degrees of the terms in decreasing order.

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