
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  $ f_m: \mathbb R \to \mathbb R$ ,  $ f_m(x)\equal{}(m^2\plus{}m\plus{}1)x^2\minus{}2(m^2\plus{}1)x\plus{}m^2\minus{}m\plus{}1,$  where  $ m \in \mathbb R$ .

1) Find the fixed common point of all this parabolas.

2) Find  $ m$  such that the distance from that fixed point to  $ Oy$  is minimal.

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