
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 line \( y = 2x + 4 \) intersects the \( y \)-axis at \( R \). A second line, parallel to the \( y \)-axis, is drawn through \( P(p, 0) \), with \( p > 0 \). These two lines intersect at \( Q \).

(a) Determine the length of \( OR \). (Note that \( O \) is the origin \( (0,0) \).)

(b) Determine the coordinates of point \( Q \) in terms of \( p \).

(c) If \( p = 8 \), determine the area of \( OPQR \).

(d) If the area of \( OPQR \) is 77, determine the value of \( p \).

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