
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 all the parentheses in the expression \((1+x)^{9}+(1+x)^{10}+\ldots+(1+x)^{14}\) are expanded and like terms are combined, a certain polynomial is obtained. Determine the coefficient of \(x^{9}\) in this polynomial, without expanding the parentheses.

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