
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
Find the solution to the equation $\left( \frac{3}{5} \right)^{x}+\left( \frac{4}{5} \right)^{x}=1$. The following solution approach is proposed: Let the function $f(x)=\left( \frac{3}{5} \right)^{x}+\left( \frac{4}{5} \right)^{x}$, then the function $f(x)$ is monotonically decreasing over $\mathbb{R}$, and $f(2)=1$, so the original equation has a unique solution $x=2$. Analogously, the solution set of the equation $x^{6}+x^{2}=(2x+3)^{3}+2x+3$ is __________.

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