
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
\[ 7.38 \quad 7.38 x^{\log _{x^{2}}\left(x^{2}-1\right)}=5 \]

\[ 7.39 \quad \left\{\begin{array}{l}3^{2 x}-2^{y}=725 \\ 3^{x}-2^{\frac{y}{2}}=25\end{array}\right. \]

\[ 7.40 \quad \left\{\begin{array}{l}(x+y) 2^{y-2 x}=6.25 \\ (x+y)^{\frac{1}{2 x-y}}=5\end{array}\right. \]

\[ 7.41 \quad \left\{\begin{array}{l}2^{\frac{x-y}{2}}+2^{\frac{y-x}{2}}=2.5 \\ \lg (2 x-y)+1=\lg (y+2 x)+\lg 6\end{array}\right. \]

\[ 7.42 \quad \left\{\begin{array}{l}\log _{4} x-\log _{2} y=0 \\ x^{2}-2 y^{2}-8=0\end{array}\right. \]

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