
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 a right triangle, the hypotenuse \(c\) is one more than twice the length of one of the legs \(a\). The square of the other leg \(b\) is:
**A)** \(2a^2 + 2a + 1\)  
**B)** \(4a^2 + 3a + 1\)  
**C)** \(3a^2 + 4a + 1\)  
**D)** \(a^2 + 4a + 4\)  
**E)** None of these

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