
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
Point \( O \) is at the origin and points \( P(a, b) \) and \( Q(c, d) \) are in the first quadrant. The slope of \( OP \) is \( \frac{12}{5} \) and the length of \( OP \) is \( 13t \). The slope of \( OQ \) is \( \frac{3}{4} \) and the length of \( OQ \) is \( 10t \). What is \( a + c \)?

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