
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 the graph of the function \( y = x^2 \) is translated by the vector \( \vec{a} = (m, 1) \) to form a new graph, and the tangent lines to the original graph and the new graph at \( x = 1 \) are perpendicular to each other, find the value of the real number \( m \).

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