
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
If $x$, $y$, and $z$ are in the ratio $3:4:6$, and it is given that $y = 15a + 5$. Also, the sum of $x$, $y$, and $z$ is 52. Find the value of $a$.
A) \(\frac{12}{15}\)
B) \(\frac{13}{15}\)
C) \(\frac{11}{15}\)
D) \(\frac{14}{15}\)

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