
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 a quadratic function  $y$  with respect to  $x$ .   $y$  takes the values of  $-1, -2$  and  $1$  for the values of  $x=-1,\ 0,\ 1$  respectively.
Find the length of the line segment of the graph of the curve cut by the  $x$ -axis.

1956 Tokyo Institute of Technology entrance exam

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