
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
Let  $V$  be the set of all continuous functions  $f\colon [0,1]\to \mathbb{R}$ , differentiable on  $(0,1)$ , with the property that  $f(0)=0$  and  $f(1)=1$ . Determine all  $\alpha \in \mathbb{R}$  such that for every  $f\in V$ , there exists some  $\xi \in (0,1)$  such that
\[f(\xi)+\alpha = f'(\xi)\]

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