
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 that triangle \( \triangle ABC \) has side lengths AB = 12, AC = 7, BC = 10, determine the effect on the area and height of the triangle when the lengths of AB and AC are each doubled, while BC remains the same.

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