
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
Calculate the following values:
1. If the binomial coefficients of the 9th and 10th terms in the expansion of $\left( \sqrt{x}+\frac{2}{\sqrt[3]{x}} \right)^n$ are equal, find the coefficient of the linear term of $x$.
2. Given $\left( 2x-1 \right)^7=a_0x^7+a_1x^6+a_2x^5+\cdots+a_7$, find the value of $a_1+a_3+a_5+a_7$.

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