
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
1. Calculate the sum: ${C_{5}^{0}+C_{6}^{5}+C_{7}^{5}+C_{8}^{5}+C_{9}^{5}+C_{10}^{5}}$
2. If $\frac{1}{C_{5}^{m}}-\frac{1}{C_{6}^{m}}=\frac{7}{10C_{7}^{m}}$, find $C_{8}^{m}$

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