
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

Find the minimum value of the following expression:
$$
\max _{0 \leq x_{1} \leq 1}\left|F_{1}\left(x_{1}\right) + F_{2}\left(x_{2}\right) + \ldots + F_{2017}\left(x_{2017}\right) - x_{1} x_{2} \ldots x_{2017}\right|
$$
(for all possible real-valued functions \( F_{i}(t) \), where \( 1 \leq i \leq 2017 \) and \( 0 \leq t \leq 1 \)).

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