
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 each interior angle of a $n$-sided regular polygon is $140^{\circ}$, find $n$.

If the solution of the inequality $2 x^{2}-n x+9<0$ is $k<x<b$, find $b$.

If $c x^{3}-b x+x-1$ is divided by $x+1$, the remainder is -7, find $c$.

If $x+\frac{1}{x}=c$ and $x^{2}+\frac{1}{x^{2}}=d$, find $d$.

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