
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 $f(x)$ be an even function defined on $\mathbb{R}$, and when $x \geqslant 0$, $f(x)=e^{x}$, if for any $x \in [a, a+1]$, the inequality $f(x+a) \geqslant f^{2}(x)$ always holds, determine the maximum value of the real number $a$.

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