
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 the functions $f(x)=x+e^{x-a}$ and $g(x)=\ln (x+2)-4e^{a-x}$, where $e$ is the base of the natural logarithm. If there exists a real number $x_{0}$ such that $f(x_{0})-g(x_{0})=3$, find the value of the real number $a$.

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