
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
Suppose a continuous function  $f:[0,1]\to\mathbb{R}$  is differentiable on  $(0,1)$  and  $f(0)=1$ ,  $f(1)=0$ . Then, there exists  $0<x_0<1$  such that  $$ |f'(x_0)| \geq 2018 f(x_0)^{2018} $$  

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