
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
"Solve the equation $( \dfrac {3}{5})^{x}+( \dfrac {4}{5})^{x}=1$." The following thought process is used: Let $f(x)=( \dfrac {3}{5})^{x}+( \dfrac {4}{5})^{x}$, then $f(x)$ is monotonically decreasing over $\mathbb{R}$, and since $f(2)=1$, the original equation has a unique solution $x=2$. Analogously, the solution set for the inequality $x^{6}-(x+2) > (x+2)^{3}-x^{2}$ is \_\_\_\_\_\_.

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