
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 $f(x) = -ax + x + a$, where $x \in (0,1]$ and $a \in \mathbb{R}^*$,

(1) If $f(x)$ is an increasing function on $(0,1]$, find the range of values for $a$;

(2) Find the maximum value of $f(x)$ on $(0,1]$.

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