
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
Consider a quadratic function \( h(x) = -x^2 - 4x + 1 \).

Define two new functions based on \( h \):
- \( j(x) = -h(x) \)
- \( k(x) = h(-x) \)

Given that \( c \) is the number of points where the graphs of \( y = h(x) \) and \( y = j(x) \) intersect, and \( d \) is the number of points where the graphs of \( y = h(x) \) and \( y = k(x) \) intersect, calculate \( 10c + d \).

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