
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
Let $\{a_n\}$ be an arithmetic sequence, and $\{b_n\}$ be a geometric sequence. Denote the sum of the first $n$ terms of $\{a_n\}$ and $\{b_n\}$ as $S_n$ and $T_n$, respectively. Given that $a_5 = b_5$, $a_6 = b_6$, and $S_7 - S_5 = 4(T_6 - T_4)$, find the value of $$\frac{a_7 + a_5}{b_7 + b_5}.$$

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