
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 the function $f(x)$ defined on $\mathbb{R}$ has a period of $2$, and satisfies $f(x)=\begin{cases} x+a, & -1\leqslant x < 0, \\ \left| \frac{2}{5}-x \right|, & 0\leqslant x < 1, \\ \end{cases}$ If $f\left( -\frac{5}{2} \right)=f\left( \frac{9}{2} \right)$, calculate $f(5a)$.

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