
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
Solve the following system of equations without using logarithms:

$$
a^{7 x} \cdot a^{15 y}=\sqrt{a^{19}}, \quad \sqrt[3]{a^{25 y}}: \sqrt{a^{13 x}}=\sqrt[12]{a}
$$

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