
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
The equation \( x^{2} - 7x + k = 0 \) has solutions \( x = 3 \) and \( x = a \). The equation \( x^{2} - 8x + (k + 1) = 0 \) has solutions \( x = b \) and \( x = c \). What is the value of \( a + bc \) ?

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