
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
A parabola passes through the point of intersection of the lines with the equations \( y = -x + 3 \) and \( x - 2y - 6 = 0 \), as well as the \( x \)-intercepts of each line. If the parabola also passes through the point \( (10, k) \), what is the value of \( k \)?

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