
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
In the diagram, what is the perimeter of polygon $ABCDE$?
```
    D ________________ E
    |                 |
    |                 |
    |                 |
    |                 |
    |                 |
    A-----------------B
    |                 |
    |                 |
    |                 |
    C_________________|
```
$A = (0,10)$, $B = (10,10)$, $C = (10, 0)$, $D = (0,5)$, $E = (10,5)$. Given lengths are $AB = 10$, $BC = 10$, and $CD = 5$. $\angle ABC = 90^\circ$ and $\angle CDE = 135^\circ$.

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