
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 $2$, in the interval $[1,3]$, $f(x)= \begin{cases}x+ \frac {a}{x}, & 1\leqslant x < 2 \\ bx-3, & 2\leqslant x\leqslant 3\end{cases}$, and $f( \frac {7}{2})=f(- \frac {7}{2})$, find the value of $15b-2a$.

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