
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
If $100a = 35^{2} - 15^{2}$, find $a$.

If $(a-1)^{2} = 3^{4b}$, find $b$.

If $b$ is a root of $x^{2} + cx - 5 = 0$, find $c$.

If $x + c$ is a factor of $2x^{2} + 3x + 4d$, find $d$.

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