
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 $f(x)=e^{x}-ax-1$ where $a \in \mathbb{R}$:

(I) Discuss the monotonicity of $f(x)$;

(II) Assuming $a > 1$, does there exist a positive real number $x$ such that $f(x) > 0$? If such an $x$ exists, find one that satisfies the condition; if not, explain why.

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