
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
The obtuse angle formed by the hands of a clock at $10:30$ is $(100+a)^{\circ}$. Find $a$.

The lines $a x + b y = 0$ and $x - 5 y + 1 = 0$ are perpendicular to each other. Find $b$.

If $(b+1)^{4}=2^{c+2}$, find $c$.

If $c-9=\log _{c}(6d-2)$, find $d$.

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