
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 the function $f(x) = \begin{cases} x^2 - 2x + 2, & x \geq a \\ 1 - x, & x < a \end{cases}$, where $a > 0$, if $f(1) + f(-a) = \frac{5}{2}$, find the value of the real number $a$.

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