
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
Given that the function $f(1+x)$ is an even function defined on the domain $\mathbb{R}$, and $f(2)= \frac {1}{2}$, where $f′(x)$ is the derivative of $f(x)$. If for all $x \in \mathbb{R}$, $f′(x) < e^x$, then the solution set of the inequality $f(x) < e^{x}- \frac {1}{2}$ (where $e=2.718\ldots$) is \_\_\_\_\_\_.

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