
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) Solve the inequality $3P_x^3 \leq 2P_{x+1}^2 + 6P_x^2$.
(2) Given $\frac {1}{ C_{5}^{m} } - \frac {1}{ C_{6}^{m} } = \frac {7}{10 C_{7}^{m}}$, find $C_{8}^{m}$.

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