Consider a computer system with a $2-$level cache hierarchy. The L$1$ cache has a latency of $1$ nanosecond $($ns$)$ and a hit rate of $90\%,$ while the L$2$ cache has a latency of $5$ ns and a hit rate of $80\%.$ The main memory access time is $50$ ns$.$ Assume that the miss penalty for the L$1$ cache is $20$ ns$,$ and for the L$2$ cache, it is $100$ ns$.$

$1.$ Determine the average access time for the $2-$level cache system, considering both cache hits and misses.

$2.$ Calculate the effective access time if the L$1$ cache hit rate is improved to $95\%$ without changing any other parameters.

Provide your answers as a single number with two decimal digits, expressed in nanoseconds $($no units$)$