= Solution
Take the <stopping times>
$$
\boxed{S_n=\inf\{t\geq0:|M_t|\geq n\},\qquad\inf\varnothing=\infty.}
$$
Continuity gives $|M_{t\wedge S_n}|\leq n$, with no overshoot at the first crossing. Stopping preserves the <local martingale> property, and the bounded case proved in question 4(i) makes each $M^{S_n}$ a continuous true <martingale>.
Every continuous path is bounded on each compact time interval, so $S_n\uparrow\infty$ <almost surely>. Hence this is also a <localizing sequence> consisting of bounded stopped <martingales>.
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