
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 $3^{x}+4^{x}=5^{x}$. The given solution approach is as follows: Let $f(x)=( \frac {3}{5})^{x}+( \frac {4}{5})^{x}$, then $f(x)$ is strictly decreasing on $\mathbb{R}$, and $f(2)=1$, thus the original equation has a unique solution $x=2$. By analogy, the solution to the equation $x^{3}+x= \frac {1}{x^{3}}+ \frac {1}{x}$ is \_\_\_\_\_\_.

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