
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
Translate a parabola $M_1$: $y = ax^2 + c$ to get another parabola $M_2$. $M_2$ passes through the vertex $A$ of $M_1$, and the axis of symmetry of $M_2$ intersects parabolas $M_1$ and $M_2$ at points $B$ and $C$ respectively. If the coordinates of point $C$ are $(2, c-5)$, then the area of $\triangle ABC$ is __________.

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