
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
Given that $f(x)$ is a function defined on $\mathbb{R}$ with a period of 2, for the interval $[1, 3]$, $f(x)$ is provided by the following piecewise expression:
$$
f(x) =
\begin{cases}
x + \frac{a}{x}, & 1 \leq x < 2 \\
bx - 3, & 2 \leq x \leq 3
\end{cases}
$$
and also $f\left(\frac{7}{2}\right)=f\left(-\frac{7}{2}\right)$. Find the value of $15b - 2a$.

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