
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
Repeat in a loop:

$$
\begin{aligned}
& \left(a_{\text{new}}, b_{\text{new}}\right):=\left(a_{\text{old}}, b_{\text{old}}\right)-\alpha \operatorname{grad} I\left(a_{\text{old}}, b_{\text{old}}\right) \\
& \left(a_{\text{old}}, b_{\text{old}}\right):=\left(a_{\text{new}}, b_{\text{new}}\right) .
\end{aligned}
$$

The choice of the parameter $\alpha$ responsible for the shift magnitude affects the convergence of the method to the minimum of the function $I(a, b)$.

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