
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 real numbers $a$, $b$, and $c$ satisfy the inequalities: $|a| \geq |b-c|$, $|b| \geq |a+c|$, $|c| \geq |a-b|$. The parabola $y = ax^2 + bx + c$ always passes through a fixed point $M$. The coordinates of point $M$ are.

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