
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 with the sum of the first $n$ terms denoted as $A_{n}$, and let $\{b_{n}\}$ be a geometric sequence with the sum of the first $n$ terms denoted as $B_{n}$. If $a_{3}=b_{3}$, $a_{4}=b_{4}$, and $\frac{{A}_{5}-{A}_{3}}{{B}_{4}-{B}_{2}}=7$, then $\frac{{a}_{5}+{a}_{3}}{{b}_{5}+{b}_{3}}=$____.

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