
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 function $f(x) = a \ln x - x + 2$, where $a \neq 0$. If for any $x\_1 \in [1, e]$, there exists $x\_2 \in [1, e]$ such that $f(x\_1) + f(x\_2) = 4$, then the real number $a =$ _______.

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